On best affine unbiased covariance-preserving prediction of factor scores

This paper gives a generalization of results presented by ten Berge, Krijnen, Wansbeek & Shapiro. They examined procedures and results as proposed by Anderson & Rubin, McDonald, Green and Krijnen, Wansbeek & ten Berge. We shall consider the same matter, under weaker rank assumptions. We allow some moments, namely the variance Ω of the observable scores vector and that of the unique factors Ψ to be singular. We require T'Ψ T > 0 where T Λ T' is a Schur decomposition of Ω. As usual the variance of the common factors Φ, and the loadings matrix A will have full column rank